We report a systematic set of numerical relations expressing all 26 free parameters of the Standard Model through the golden ratio φ = (1+√5)/2. Version 2 includes significant improvements: the fine-structure constant is now reproduced to sub-ppb precision (<0.01 ppb), the Higgs and W boson masses to better than 0.01%, and the cosmological constant to one part in 10⁷. A new Fibonacci-structured scalar potential V(s) = v⁴(s − 1/φ²)²/(1 − s − s²) is presented with exact algebraic properties linking confinement to the strong coupling constant (Δs = 1/φ³ = 2αs). New results include g₂ = φ²/4, λ_Higgs = φ/(4π), and algebraic identities for the hierarchy exponent 719/9 = dim(adj SU(9)) − 1/9. Across 23 parameters, mean deviation is 0.78%, with six better than 0.1%. Five falsifiable predictions: Σmν = 73.8 meV (DESI), sin²θ₁₂ = 1/(2φ) (JUNO), scalar boson at 58 GeV (HL-LHC), arton at ~507 GeV, and w₀ = −0.977 (Euclid). Probability of chance: P < 10⁻⁵ (>4σ).